Question

In each of the figures below, a light beam from hits a double slit plate with a separation of s or 2s. After that, it travels a distance until it hits a screen, creating an interference pattern on a screen. The interference pattern is shown on the diagram, where the constructive wave peaks are visible and the destructive wave troughs are not. The distance to the screen and the separation of peaks is given in the figure. Rank the wavelength of the light in situations A-F, breaking ties alphabetically. (A) (B) (c) d d > 2w 4w 3w 2s 2s (D) (E) (F) 2d 2d 2d 3w > 2w 4w

Answer 1

Let slit separation = s

distance to screen = d

Then fringe width $w = \frac{\lambda d}{s}$

so wavelength

US X d

(A)

   $\lambda_A = \frac{2ws}{d} \\ \lambda_A = 2\lambda$

(B)

                $\lambda_C = \frac{4w*2s}{d} \\ \lambda_C = 8\lambda$

(C)

$\lambda_C = \frac{3w*s}{d} \\ \lambda_C = 3\lambda$

(D)

$\lambda_D = \frac{3w*2s}{2d} \\ \lambda_D = 3\lambda$

(E)

$\lambda_E = \frac{2w*s}{2d} \\ \lambda_E = \lambda$

(F)

$\lambda_F = \frac{4w*2s}{2d} \\ \lambda_F = 4\lambda$

So Rank is

B > F > C = D > A > E

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mention in comment box if you have any doubt